Question: Simplify the following expression: $p = \dfrac{-7q^2 - 112q - 441}{q + 7} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ p =\dfrac{-7(q^2 + 16q + 63)}{q + 7} $ Then we factor the remaining polynomial: $q^2 + {16}q + {63} $ ${7} + {9} = {16}$ ${7} \times {9} = {63}$ $ (q + {7}) (q + {9}) $ This gives us a factored expression: $\dfrac{-7(q + {7}) (q + {9})}{q + 7}$ We can divide the numerator and denominator by $(q - 7)$ on condition that $q \neq -7$ Therefore $p = -7(q + 9); q \neq -7$